# Useful Maths Number system Shortcuts (For IBPS, SSC, GOVERNMENT EXAMS)

**Useful Number system Shortcuts.**

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1. When Sum and Diff of two numbers (X and Y) are given,

then

X = (sum + diff)/2

Y = (sum – diff)/2

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2. Diff between two digits of two

digit number is =(Diff in original and interchanged number)/9

.

3. Sum of first n odd nos is n2

.

4. Sum of first n even nos n(n+1)

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5. Sum of squares of first n natural no’s is n(n+1)(2n+1)/6

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6. Sum of cubes of first n natural numbers is [n(n+1)/2]2

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7. If the sum of squares of two numbers is x and the square of their diff is y, then the product of the two numbers is [(x-y)/2]

.

*********Ratio and Proportion Short-cuts*********

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1. If four quantities are in proportion, then Product of Means = Product of Extremes. In the proportion a:b::c:d, we have bc = ad

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2. If a:b::c:x, x is called the fourth proportional of a, b, c. a/b = c/x or, x = bc/a.

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3. If two numbers are in a:b ratio and the sum of these numbers is x, then numbers will be ax/ (a+b) and bx/(a+b) respectively

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4. If three numbers are in the ratio a:b:c and the sum of these numbers is x, then these

numbers will be ax/(a+b+c) , bx/(a+b+c) and cx/(a+b+c) respectively

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5. If the ratio of two numbers is a: b, then the numbers that should be added to each of the numbers in order to make this ratio c:d is given by (ad-bc)/(c-d)

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6. If the ratio of two numbers is a:b, then the number that should be subtracted from each of the numbers in order to make this ratio c:d is given by (bc-ad)/(c-d)